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Contract No. DE-AC36-08GO28308

Comparison of the Accuracy 

and Speed of Transient Mobile 

A/C System Simulation Models

Preprint

T. Kiss and J. Lustbader

National Renewable Energy Laboratory

To be presented at the SAE 2014 World Congress and Exhibition

Detroit, Michigan

April 7-11, 2014

Conference Paper

NREL/CP-5400-61045

March 2014
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Comparison of the Accuracy and Speed of Transient Mobile A/C System 

Simulation Models

Tibor Kiss and Jason Lustbader

National Renewable Energy Laboratory

Abstract

The operation of air conditioning (A/C) systems is a significant 

contributor to the total amount of fuel used by light- and heavyduty vehicles. Therefore, continued improvement of the 

efficiency of these mobile A/C systems is important. Numerical 

simulation has been used to reduce the system development 

time and to improve the electronic controls, but numerical 

models that include highly detailed physics run slower than 

desired for carrying out vehicle-focused drive cycle-based 

system optimization. Therefore, faster models are needed 

even if some accuracy is sacrificed. 

In this study, a validated model with highly detailed physics, 

the “Fully-Detailed” model, and two models with different levels 

of simplification, the “Quasi-Transient” and the “MappedComponent” models, are compared. The Quasi-Transient 

model applies some simplifications compared to the FullyDetailed model to allow faster model execution speeds. The 

Mapped-Component model is similar to the Quasi-Transient 

model except instead of detailed flow and heat transfer 

calculations in the heat exchangers, it uses lookup tables 

created with the Quasi-Transient model. All three models are 

set up to represent the same physical A/C system and the 

same electronic controls. Speed and results of the three 

model versions are compared for steady state and transient 

operation. Steady state simulated data are also compared to 

measured data.

The results show that the Quasi-Transient and MappedComponent models ran much faster than the Fully-Detailed

model, on the order of 10- and 100-fold, respectively. They 

also adequately approach the results of the Fully-Detailed

model for steady-state operation, and for drive cycle-based 

efficiency predictions 

Introduction

When operated, the A/C system is the largest auxiliary load on 

a vehicle. A/C loads account for more than 5% of the fuel used 

annually for light-duty vehicles in the United States [1]. A/C 

loads can have a significant impact on hybrid electric vehicle, 

plug-in hybrid electric vehicle, and electric vehicle 

performance. Hybrid electric vehicles have 22% lower fuel 

economy with the A/C on [2]. Mitsubishi reports that the range 

of the i-MiEV can be reduced by more than 45% on the Japan 

10–15 cycle when the A/C is operating [3]. The advanced 

powertrain research facility at Argonne National Laboratory has 

reported an 18% reduction in range for the Nissan Leaf 

operating on the UDDS cycle with 35°C ambient and 850 

[W/m2

] solar simulator loading [4]. Increased cooling demands 

from the battery thermal management system in an electric 

vehicle may also add additional loads on the A/C system. Air 

conditioning in heavy-duty vehicles also uses significant fuel 

for both idle [5] and down-the-road operation. A flexible opensource analysis tool is needed to assess the A/C system 

impact on advanced vehicles. Industry has expressed a need 

for both a standalone A/C system model as well as an A/C 

model that can co-simulate with a vehicle simulator such as 

Autonomie [6]. 

The A/C system contains complex flow, thermodynamics, and 

heat transfer. On the refrigerant side, the flow is transient and 

both compressible and two-phase. Calculating refrigerant 

properties near the phase transitions can also be 

computationally difficult. Air flow through the condenser can 

vary widely depending on vehicle speed and condenser fan 

speed. The heat transfer in the heat exchangers is a very 

complex process mainly addressed by complex correlations 

based on measured data. These correlations sometimes 

reduce the stability of the code. The effects of humidity and 

water condensation are difficult to account for, not only in the 

model but also for the experimental data necessary to calibrate 

the code. A cabin model is also needed to provide a realistic 

load on the evaporator. The cabin model must consider all the 

major pathways of heat transfer into the cabin, including solar 

and convective loads from the environment, heat from the 

engine compartment, and sensible and latent heat loads in the 

air stream. Realistic control methods similar to ones actually 

used in automotive A/C systems also have to be implemented. 

The cycling of the compressor can introduce quick transients 

that are sometimes difficult to handle by the numerical solver. 

The simulation model also has to be fast enough for the 

purpose of evaluating vehicle power performance and/or the 

design of A/C systems and their controls. 

There are numerous challenges in developing a suitable 

automotive A/C system simulation tool. Some examples of 

previously developed non-commercial full system-level 

simulation include [7, 8, and 9]. However, to the best of our 

knowledge, none of these or other models have been

developed in the widely used dynamic system simulation 

platform MATLAB/Simulink. Using this platform has several 

advantages. Autonomie is also built on Simulink, which 

facilitates integration of the model into Autonomie. 

MATLAB/Simulink is widely used in industry, so the 

standalone, freely available version of the A/C model can be 

widely distributed. To address these needs, the authors 
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developed a 1-D finite volume A/C system simulation model in 

the Matlab/Simulink environment and compared it to steady 

state data [10]. 

This “Fully-Detailed” model provided good agreement with data 

but ran 10 times slower than real time. It was clear the model 

was too slow for practical vehicle drive cycle based evaluation. 

Therefore, the need arose to develop new model versions that 

provided much faster execution speed while minimizing the 

loss in accuracy (Figure 1). Drive cycle based studies are 

especially well suited for such compromise – short transients 

are less important as long as averaged values for heat transfer 

rate and compressor power are accurately predicted over long 

periods of simulation time. 

To match an appropriate balance of speed and accuracy with

the various A/C modeling needs, two additional complementary 

models were developed, the Quasi-Transient and the MappedComponent model. The user can switch between these models 

to match the model detail with the current needs of a project. 

The Quasi-Transient model runs 10 times faster and 

theoretically matches the steady state conditions of the FullyDetailed model, but will lose some accuracy during transients. 

The Mapped-Component model is 100 times faster, but instead 

of detailed calculations of flow and heat transfer in the heat 

exchangers, these variables are obtained from multidimensional lookup tables. 

Figure 1. Three model versions to match need with accuracy and 

speed

This paper will briefly summarize the original Fully-Detailed

model; for more detail, see reference [10]. The Quasi-Transient 

and Mapped-Component models will then be described in 

detail. The results from all three models are then compared to 

steady state measured data from a light-duty A/C system. 

Finally, drive cycle averaged system variables from the three 

models will be compared. 

Approach

The new faster Quasi-Transient and the Mapped-Component 

models were developed from the original Fully-Detailed model. 

The Quasi-Transient model runs 10 times faster and 

theoretically matches the steady state conditions of the FullyDetailed model, but will lose some accuracy during transients. 

The Mapped-Component model is 100 times faster than the 

Fully-Detailed model, but instead of detailed calculations of 

flow and heat transfer in the heat exchangers, these variables 

are obtained with the help of multi-dimensional lookup tables. 

The lookup tables used in the Mapped-Component models are 

created with the evaporator and condenser sub-models of the 

Quasi-Transient model. 

Both the Quasi-Transient and the Mapped-Component models 

incorporate as much of the original Fully-Detailed model as 

possible. All the descriptions for the cabin, thermostatic 

expansion valve, and compressor sub-models as well as the 

described controls algorithm for the Fully-Detailed model apply 

to these model versions. The heat exchanger structure of the 

models is also identical between the Fully-Detailed and the 

Quasi-Transient models. The only difference between the 

Quasi-Transient and the Fully-Detailed models is that they use 

different Simulink S-functions (user-defined code) for the zerodimensional (0-D) volume and one-dimensional (1-D) pipe 

blocks. In the 1-D pipe simulation blocks, the air-side and the 

wall temperature calculations are identical for the FullyDetailed and Quasi-Transient version. The MappedComponent model differs from the Quasi-Transient model only 

in the condenser and the evaporator sub-models where simple 

multi-dimensional lookup functions are used in place of the

detailed heat exchanger models composed of 0-D volume and 

1-D pipe simulation blocks.

Fully-Detailed Model Summary

The Fully-Detailed model places an emphasis on predicting 

transient processes accurately. The model has to be robust for 

fast transients such as compressor cycling, has to accurately 

predict refrigerant redistribution after shutdown and after 

startup, and has to conserve mass accurately during 

simulations of long test cycles. The more complex and 

accurate model was also developed first to serve as a 

benchmark for understanding the error induced through 

simplifying assumptions that enable faster models. 

A finite volume formulation for calculating the refrigerant flow

was chosen because it is well suited for accurate conservation 

of mass, momentum, and energy. This accuracy is necessary 

for predicting quick transient processes correctly. 

The A/C model consists of two main sub-models, the cooling 

circuit model and the cabin model. In the cooling circuit model, 

the larger volumes containing refrigerant (e.g., the 

accumulator, the receiver/dryer, and the headers of the heat 

exchangers) are modeled with the 0-D volume simulation

block. The refrigerant pipes and the tubes (flat tubes, round 

tubes, or plates) of the heat exchangers are modeled with 

various versions of the 1-D pipe simulation block. The

refrigerant-side circuit is built up as a network of these 1-D pipe 

blocks connected to each other with 0-D volume blocks. 

In the 0-D volume block, the control volume equations for 

conservation of mass and internal energy are solved [11]. 

Because internal energy and mass are the state variables for 

the simulation, all other refrigerant properties are looked up 

from two-dimensional tables based on specific internal energy 

and density. 

In the 1-D pipe simulation blocks, on the refrigerant side, 

equations for conservation of mass, momentum, and energy 

are solved through a finite volume method. As with the 0-D 

volume block, all refrigerant properties are obtained from twodimensional tables based on specific internal energy and 

density in each finite volume (also called segments). From the 

applied finite volume method in the 1-D pipe simulation block, it 
3 

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is inherent that the refrigerant flow can take place in both 

directions. The solution method marches only in time and not

in space. The evaluation of heat transfer between the pipe wall 

and the refrigerant is through local heat transfer coefficient 

correlations. 

The 1-D pipe model simulation allows the option of multiple 

“parallel channels” on the refrigerant side and complex fin 

geometry on the external air flow side. It is assumed that the 

refrigerant flow variables inside the parallel channels are 

identical. The wall/fin temperatures in the direction of the air 

flow are assumed to be constant. 

For the air flow, there are no conservative terms and the flow is 

described with purely algebraic equations. Mass flow rate, 

temperature, and the relative humidity of the incoming wet air 

for each pipe segment are input variables. The air-side heat 

transfer equations are solved for each segment of the pipe 

using the Chang local heat transfer coefficient correlations [12]. 

The effectiveness-NTU (E-NTU) method [13] is applied on 

each segment, which ensures that the exit air temperature 

does not overshoot the wall temperature. Fin efficiency

calculations are also incorporated [13]. 

The effects of humidity and condensation, when present, are 

accounted for. First, the exit air temperature is calculated from 

the heat transfer rate as it would be without condensation. If 

the air temperature drop due to this heat transfer is sufficient to 

indicate condensation, then an iteration on the exit wet air 

temperature is invoked. During this iteration the heat transfer to 

the heat exchanger wall is still assumed to be the same as it 

would be without condensation. Once the exit wet air 

temperature is obtained, all other air flow properties can easily 

be calculated. This same process is applied to all the pipe 

segments, and the exit air flow conditions are obtained for 

each pipe segment. 

The air-side and refrigerant-side equations can be solved on 

their own separately because the two sets of equations are not 

algebraically coupled. The pipe wall temperature, Tw, appears 

in both sets of equations, but it is a simulation state variable, 

which means its value is obtained as a result of an integration 

step, not from algebraic equations. Therefore, it is available at 

the beginning of each time step to calculate the heat transfer 

rates from the air to the pipe wall and from the pipe wall to the 

refrigerant. The pipe wall temperature couples the equations 

on the refrigerant and air sides.

It is assumed that the thermal resistance of the wall is zero. In 

other words, the inner and outer surfaces of the pipe wall are 

at the same temperature. This is typically a good 

approximation for compact heat exchangers which use thin 

walls.

The equation for the wall temperature comes from the 

conservation of energy, which states that the net heat flux into 

the wall segment is stored as thermal energy in the wall 

segment:

Q̇

aw − Q̇wr − dQ̇

x

dx ∙ ∆x = Cpw ∗ ∆mw ∗

dTw

dt , (1) 

where Q̇

aw is the heat transfer rate from air to the wall, Q̇wr is 

the heat transfer rate from the wall to the refrigerant, Q̇

x is the 

heat transfer rate in the pipe wall in the refrigerant flow 

direction, Cpw is the wall material specific heat, and ∆mw is the 

mass of the wall segment including all the fins. The dQ̇

x

dx ∙ ∆x 

term represents the imbalance in conductive heat flow rates 

from the neighboring wall segments. With this equation, the 

thermal capacity of the wall has been accounted for. This 

equation is written for each pipe segment, and the wall 

temperature is obtained for each pipe segment.

The refrigerant used in the current model is R134a. The effects 

of the lubricating oil in the refrigerant circuit have not been 

accounted for.

Heat Exchangers

Compact heat exchangers are typical in automotive A/C 

systems and have a general structure that can be described as 

a number of headers, with “passes” between these headers. 

Nearly all of the heat transfer takes place in the passes. Using 

conventional terminology, one pass in the condenser consists 

of a number of round or flat tubes and one pass in the 

evaporator consists of a number of flat tubes or plates. 

Two versions of the 1-D pipe model simulation block described

above, with air-side heat transfer according to Chang’s model 

[12], are the basic building blocks for the heat exchangers in 

the A/C system model. To model the tubes of the condenser, a 

version employing the Dittus-Boelter equation [13] is used on 

the refrigerant side along the full length of the pass, even

across the phase boundaries. In the saturated mix region, the 

quality weighted averages of the saturated liquid and saturated 

vapor properties of the refrigerant are used. For the version 

used to model the plates of the evaporator, on the refrigerant

side, the Chen correlation [14] is used for the two-phase region

up to 90% quality, and the Dittus-Boelter correlation with vapor 

properties is used in the superheat region. A smooth transition 

between the two is also implemented in the 90%–100% quality 

range. The Chen correlation was selected because it was 

originally developed for boiling flow in “conventional” channels 

as defined by Kandlikar [15], but it was verified by at least two 

studies that it can be used for minichannel configurations as 

well [16,17], demonstrating a relatively wide range of 

applicability. The evaporator plates used in the current study 

fall into the conventional channel category with a hydraulic 

diameter of 8.4 mm. 

To build a heat exchanger model, each pass/subpass is 

represented with a 1-D pipe model block that is connected 

using 0-D volume blocks representing each of the headers. 

Passes are split up into sub-passes when the air inflow is 

coming from two different upstream passes. To account for the 

number of plates in each pass/subpass, the refrigerant mass 

and enthalpy flow rates have to be multiplied by the number of 

plates in the pass before being routed into the 0-D volume 

blocks representing the headers. The total heat transfer rate on 

the pass/subpass is also the product of the number of plates 

and the heat transfer rate on just one plate. Therefore, in this 

approach, all the plates in a given pass are treated as identical 

in terms of their flow and heat transfer. Figure 2 shows the 

structure of the evaporator implemented in the model.
4 

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Figure 2. The “exploded view” schematic of the implemented 

evaporator 

Routing the airflow is also relatively easy with the applied 

modeling method. The segment-wise exit air flow variables 

from a plate are passed as an output vector from the 1-D pipe 

simulation block representing the plate. If the air enters another 

pass in a downstream row, this vector—with proper alignment 

—is directly fed into the inlet air flow variables input port of the 

simulation block representing the plate in the downstream row. 

Alternatively, the exit air flow output vector is mixed with a 

special simulation block. This option can be used for the last 

row of the heat exchangers where the airflow from the plate is 

also exiting the whole heat exchanger. 

Thermostatic Expansion Valve

The expansion device implemented in the model is an 

externally balanced thermostatic expansion valve, and 

therefore a receiver/drier is also implemented in the model. 

The bulb temperature responds to changes in the evaporator 

exit temperature with a first-order delay. The characteristic time 

of this response is an input parameter to the model. 

This response is the only dynamically modeled detail. 

Otherwise, the position of the flow restriction device is 

determined from static force balance. Once the flow area 

through the flow restriction device of the valve is known, the 

refrigerant flow rate is calculated from the two-phase orifice 

flow equations, accounting for choked flow when the pressure 

drop is high enough.

Compressor

The compressor is a constant-displacement, variable-speed 

device. The rotational speed and the displacement per 

revolution (both input parameters) determine the ideal 

forwarded volume per second. Actual forwarded volume per 

second is then obtained with the application of a volumetric 

efficiency, and the refrigerant mass flow rate is the actual 

forwarded volume per second multiplied by the upstream 

density. Refrigerant upstream conditions and downstream 

pressure are input. The compression process is assumed 

adiabatic. The downstream enthalpy is calculated with the help 

of an isentropic efficiency ([18], Eq. 6-62). The compressor 

shaft power is then the rise in the enthalpy flow rate divided by

a mechanical efficiency. 

Both the volumetric and the isentropic efficiencies are functions 

of the compressor speed and the downstream-to-upstream 

pressure ratios. These tables are inputs to the model. A 

mechanical drive compressor is used with clutch cycling as 

explained in the Controls section. The compressor model can 

easily be changed to that of a variable-displacement device by 

implementing the appropriate controls. 

Cabin Model

The purpose of the cabin model is to provide a reasonably 

accurate estimate of the cabin conditions that can serve as the 

boundary conditions for the cooling circuit model. The cabin air 

is represented with a zero-dimensional lump-sum air/water 

vapor mix volume. The cabin shell and interior thermal masses 

are included. Heat transfer between the thermal masses, the 

cabin air, and the ambient air are accounted for, as well as the 

solar energy absorption by each thermal mass. The thermal 

masses and the heat transfer paths that are included in the 

model are shown in Figure 3. 

Figure 3. Schematic of the cabin model

The thermal masses are shown in the rounded boxes, and the 

heat transfer paths are shown with solid arrows. All body air 

leak flow rates are lumped together and calculated as an 

adjustable constant times the pressure differential between the 

cabin and the ambient. The cabin model schematic is shown 

with the air passages for fresh and recirculated air.

Controls

Basic electronic controls have been implemented in the model. 

Shutoff of the compressor due to downstream pressure 

passing above a high pressure limit, or upstream pressure 

passing below a low pressure limit is included. The compressor 

is also cycled on or off depending on whether the cabin 

temperature is below or above the target temperature and 

whether the evaporator-out air temperature is below or above a 

freezing limit temperature. A temperature dead-band is 

implemented for both of these control variables to reduce the 

frequency at which the cycling occurs. In addition, limits on 

how long the compressor has to stay off after each clutch-off

cycle is also implemented. The evaporator blower speed is set 

to one of a number of selectable settings and is not adjusted 

by the controls algorithm. The cabin air recirculation rate is the 

portion of air mass flow to the evaporator that is coming from 

the cabin, the rest being made up with outside air. This rate is 

set by the controls algorithm in the 5% - 95% range based on 
5 

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whether the cabin temperature exceeds the outside 

temperature or not. Alternatively, the recirculation rate can be 

set constant over the entire simulation. 

These controls are easily modified and additional control 

algorithms can be added by the user given the block simulation 

environment of Simulink

The Quasi-Transient Model

The Quasi-Transient model was created to provide an option 

for much faster model simulation speed that better facilitates 

drive cycle-based A/C system studies than the Fully-Detailed

model. It is also useful for debugging the Fully-Detailed system 

model when a new control algorithm or modified components 

are installed. This model comes at a cost of some accuracy for 

transient process predictions. The Simulink S-functions that 

constitute the heart of the simulation model and the Simulink 

“masks” that improve user communication were created such 

that any Fully-Detailed model can very quickly be converted 

into an equivalent Quasi-Transient model or vice versa. This 

conversion is done by simply swapping out the Fully-Detailed

model’s 1-D line and 0-D volume Simulink S-functions with 

their Quasi-Transient equivalents. Some straightforward 

adjustments to the initialization files also have to be made. 

For the Quasi-Transient model, some non-conservation error is 

allowed to increase the simulation speed. The approach works 

by pulling the solution towards the steady state solution that 

belongs to the boundary conditions prevailing at the current 

time step. Thereby the Quasi-Transient model approximates 

the solution that would be obtained with a hypothetical quasisteady model that in every time step calculates the steady

state conditions. The Fully-Detailed model uses a finite volume 

formulation in the refrigerant lines with marching in time only

whereas the Quasi-Transient model uses a finite volume 

method with marching in space as well as in time. When all the 

time derivatives of the flow and other variables are zero, such 

as in steady state conditions, the solutions to the equations 

incorporated in the Quasi-Transient model will closely match 

the solutions of those equations incorporated in the FullyDetailed model. 

In the 0-D volumes, a compromise is made to the accuracy of 

the implemented conservation equations. With this treatment,

however, it can be ensured that the volumes in the system 

model all have similar “stiffnesses” and high stiffness in the 

volumes with liquid is avoided. This allows for a larger 

simulation time step resulting in much faster model execution. 

The 1-D pipe model used in the Quasi-Transient model has a 

refrigerant mass flow rate that is constant along the line and is 

also a simulation state variable. In each time step, the 

refrigerant pressure drop across the line is compared to the 

pressure drop obtained from the two attached 0-D volumes. A 

numerical method is applied to continuously adjust the 

refrigerant mass flow rate in the lines to match the pressure 

drop in the line to the pressure drop between the attached 0-D 

volumes better. The refrigerant mass flow rate responds with 

some delay, but it is tending towards the flow that would 

develop under the steady state conditions. 

The cost of the approach used for the 0-D volume and 1-D 

pipe models is that the total refrigerant mass in the system is 

slightly fluctuating and the energy balance is slightly off, 

especially for shorter simulated time periods. For steady state 

conditions, however, the conservation of mass and energy for 

each 0-D volume and each 1-D pipe in the model is valid.

The equations used for the Quasi-Transient model reflect the 

goal of approximating the quasi-steady solution; that is, a 

system response solution that is a series of steady state 

solutions belonging to the current system boundary conditions. 

For example, if the system was in a steady state condition and 

a boundary condition (say cabin temperature) takes a unit step, 

the model will correctly predict the steady state conditions prior 

to the step and the new steady state conditions developed 

after the step, but not the intermediate conditions of the system 

in between. The equations and method detailed in the following 

sections will successfully produce this behavior. 

There are significant approximations involved in the QuasiTransient model; however, it provides a good balance between 

accuracy and speed. Ultimately, the utility of this model is 

determined by how fast it executes and how well it 

approximates the results of the Fully-Detailed model.

The 0-D Volume Model

To achieve the goal of the Quasi-Transient model, the concept 

of ‘artificial mass’ of the refrigerant is introduced which allows 

the adjustment of the system ‘stiffness’. The conservation 

equations are written for this artificial mass. The size of the 0-D 

volume is an input parameter and it does not change in time. 

Mass and enthalpy flow rates into and out of the volume are 

input variables. The heat transfer rate across the solid 

boundary of the volume is also an input variable. Conservation 

of artificial mass is implemented. The time derivative of the 

artificial mass in the volume is the difference between the sum 

of incoming and the sum of outgoing mass flow rates. 

dma

dt = �ṁin,i − �ṁ out,j

i j

(2) 

where ma is the artificial mass, t is time, and ṁin,i and ṁ out,j

are incoming and outgoing mass flow rates, respectively. 

Conservation of energy is handled similarly with a form of the 

control volume equation. The size of the volume is constant, 

which means there is no work on the solid boundary surfaces 

that would have to be accounted for. Therefore, the time 

derivative of the total energy in the volume is the sum of 

incoming enthalpy flow rates minus the sum of outgoing 

enthalpy flow rates plus heat addition: 

dU

dt = �Ḣ

in,i − �Ḣout,j + Q̇

i j

(3) 

where U is the internal energy, Ḣ

in and Ḣout are the enthalpy 

flow rates in and out the volume, respectively, and Q̇ is the 

heat transfer rate into the volume through the walls. 
6 

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Then naturally, ma and U are the simulation state variables. 

From Eqs. (2) and (3), the integrator can generate the artificial 

mass and total energy, so these are obtained before any other 

variables as time is advanced by one time step.

The introduction of the artificial refrigerant mass opens up the 

possibility to change how pressure and density are connected 

through the refrigerant material property equations; in fact, this 

is the reason behind introducing the artificial mass. In this 

model, the refrigerant in the volume is represented by one 

single bulk modulus valid for all conditions. With that, the 

pressure is a function of the artificial density only. The bulk 

modulus is also proportional to the size of the volume. This 

ensures that the volumes in the system model all have 

adjustable and identical ‘stiffness’. Equal “stiffness” in all the 

volumes means that the addition of unit refrigerant mass to any 

of the 0-D volumes in the system will result in the same

pressure rise. With this treatment, high stiffness in the volumes 

with pure liquid present is avoided. The result is a higher 

simulation time step allowed and therefore a much faster 

model execution. Accordingly, the pressure is

p = B ∙ �

ma/V

ρref

− 1� (4) 

where B is the bulk modulus, V is the size of the volume and 

ρref is a reference density. Note that while V is varying from 

volume to volume in the model, B/V is the same for each 

refrigerant volume (0-D volume) in the model. B/V is an input 

parameter as well as the volume, and B is calculated. The 

lower the value that is given to B/V, the “softer” the system will 

be. By dividing the total enthalpy with the artificial mass, the 

specific enthalpy in the volume can be obtained as

h = (U + pV)/ma (5) 

Temperature is calculated from the pressure and the specific 

enthalpy, based on the property tables. The “actual” density or 

just density is also calculated. It is noted that this density is not 

the artificial density that comes from the artificial mass divided 

by the volume, but instead, like the temperature, is calculated 

from the pressure and specific enthalpy using the accurate 

property tables. This is done so that the true refrigerant mass 

in the system, the one that is consistent with the pressures and 

enthalpies all over the system, can be evaluated. 

It should be noted that Eqs. (2) and (3) reduce to the accurate 

equations for conservation of mass and energy when applied 

to steady state conditions. In addition, the model in every time 

step—if the boundary conditions are frozen—would start 

converging to the steady state solution belonging to those 

frozen boundary conditions. 

To this latter point the following observations can be made. If 

the sum of incoming mass flow rates is greater than the sum of 

outgoing mass flow rates, the artificial mass will increase, and 

therefore the pressure in the volume will increase. This 

pressure rise will reduce the incoming mass flow rates and will 

increase the outgoing mass flow rates. In the end, the system 

will change in the direction of the incoming and outgoing mass 

flow rates to become more equal, that is, towards a steady 

state solution. A similar statement can be made for the 

enthalpy exchange, at least for the case when the mass flow 

rates already reached steady state. Then, if the sum of the 

enthalpy inflow rates plus the heat transfer rate is greater than 

the sum of the enthalpy outflow rates, the internal energy in the 

volume will rise, which will increase the outgoing enthalpy flow 

rates but will not affect the incoming enthalpy flow rates. The 

result is again that the system variables are changed in the 

direction of the steady state solution. 

Therefore, Eqs.(2) and (3) reduce to the rigorous mass and 

energy conservation equations in steady state conditions and 

they will move the system towards the correct steady state 

conditions from any transient conditions.

The 1-D Pipe Model

These equations were also developed with the goal of

approximating the quasi-steady solution. In such a solution, the 

refrigerant mass flow rate is constant along the length of the 

pipe at any time, although it varies in time. As was mentioned 

earlier, on the air side and for the wall temperature 

calculations, this 1-D pipe model is identical to the 1-D pipe 

model of the Fully-Detailed model.

A finite volume formulation is used again to determine the 

lengthwise distribution of flow parameters, and this requires 

splitting up the line into finite volumes or “segments.” With the 

refrigerant mass flow rate fixed along the length of the pipe, the 

finite volume equations can be applied with a marching 

scheme in the direction of the flow. For each segment and in 

each time step, the flow variables on the outlet boundary of a 

segment can be calculated from the flow variables on the inlet 

boundary of the segment and the wall temperature of the 

segment. Assume for now that the magnitude and direction of 

the refrigerant mass flow rate is known as we start calculating 

the distributed flow parameters. Then the inlet boundary 

conditions of the first segment are those prevailing in the 0-D 

volume attached on the upstream side of the 1-D pipe block. 

No slip velocity is assumed, and the flow is assumed to be 

homogeneous.

First the pressure on the exit boundary of the segment, pout, is 

calculated using the Darcy-Weisbach equation ([11], Eq.

5.8.7). 

pout = pin − 1

2� f

L

DH

ρinvin

2 (6) 

where pin, ρin, and vin are the pressure, the density, and the 

velocity on the inlet boundary of the segment; L is the length of 

the segment; and Dh is the hydraulic diameter. vin is the 

constant mass flow rate, ṁ , divided by the inlet boundary 

density, ρin. The wall friction coefficient, f, is obtained from the 

Hagen-Poisseuille equation ([11], Eq. 5.10.12) for laminar flow 

and from a modified version of the Colebrook equation ([11], 

Eq. 5.10.13) for turbulent flow, always using the inlet boundary

flow variables. When two-phase flow is present on the inlet 

boundary of the segment, viscosity is a quality averaged value 

of the saturated vapor and saturated liquid viscosities at the 

inlet boundary temperature. In accordance with the above, no 

void fraction based correlation was implemented for the 

pressure drop calculation. It is noted that the pressure drop 
7 

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calculation used the same basic equations as the FullyDetailed model.

Next the local heat transfer coefficient is calculated with 

essentially the same correlations as for the Fully-Detailed 

model. When two-phase flow prevails on the inlet boundary, 

refrigerant material properties are the quality weighted average 

of the saturated liquid and saturated vapor properties. The 

default for calculating the local heat transfer coefficient is the 

Dittus-Boelter correlation [13]. For only the two-phase boiling 

flow in the evaporator plates, the Chen correlation [14] is used.

If single-phase flow prevails on the inlet boundary, the E-NTU 

method [13] as applied for constant wall temperature is used in 

the refrigerant flow direction to obtain the exit temperature. 

This ensures the exit temperature from the segment does not 

overshoot the wall temperature and that no restriction needs to 

be placed on the length of the segment from a stability point of 

view:

Tout = Tin − (Tin − Tw) ∙ �1 − exp

αA

ṁ Cp

� (7) 

where Tin is temperature on the inlet boundary, Tw is the 

segment wall temperature, A is the heat transfer area (segment 

length times inner channel perimeter) α is the heat transfer 

coefficient and Cp is the constant pressure specific heat. It is 

possible, however, that the flow is single phase on the inlet 

boundary, but turns into two-phase flow within the segment. 

For example, the location at which condensation starts in the 

condenser does not have to line up with a segment boundary. 

Therefore, a check has to be carried out using the exit 

temperature predicted by Eq. (7). For the condenser example, 

it is checked whether Tout > Tsat(pout). If yes, then there is no 

phase region change, the Tout calculated in Eq. (7) stands, and

the heat exchange rate from the refrigerant to the wall can be 

calculated as 

Q̇ = Cp ∙ ṁ ∙ (Tin − Tout) (8) 

If, on the other hand, Tout < Tsat(pout), the refrigerant is 

moving from superheated vapor into the saturated mix region 

at some location within the segment. In this case, the distance 

from the inlet boundary, y at which Tout = Tsat(pout), is 

determined using the E-NTU equation, Eq. (7), but substituting

A = y ∙ w (w is the internal flow path perimeter) and solving for

y. Then the heat transfer rate in the single-phase section of the 

segment is 

Q̇

1 = ṁ ∙ �hin − hsat,v(pout)� (9) 

where hin is the enthalpy on the inlet boundary, and hsat,v is 

the saturated vapor enthalpy. The heat transfer rate in the twophase region part of the segment is calculated as 

Q̇

2 = A ∙

L − y

L ∙ α ∙ (Tsat(pout) − Tw) (10) 

The total heat transfer in the segment is 

Q̇ = Q̇

1 + Q̇2 (11) 

Once the heat transfer rate is determined either with Eq. (8) or 

Eq. (11), the specific enthalpy on the outlet boundary can be 

calculated with 

hout = (Ḣ

in − Q̇

)/ṁ (12) 

where Ḣ

in is the enthalpy flow rate through the inlet boundary 

of the segment. From hout and pout all other refrigerant 

properties can be calculated on the outlet boundary. 

If there is saturated mix on the inlet boundary, then the 

temperature change in the segment is likely minimal, and a 

different method has to be used. The segment exit pressure, 

pout, is again calculated with Eq. (6). The temperature of 

refrigerant at the exit is that of the saturated mix temperature at 

the segment exit pressure, it is not coming from the heat 

transfer rate. A constant temperature difference along the 

segment between the wall and the refrigerant can be assumed 

and the heat transfer rate from refrigerant to the wall can be 

calculated without the E-NTU method simply as 

Q̇ = A ∙ α ∙ (Tin − Tw) (13) 

The enthalpy outflow rate is

Ḣ

out = Ḣin − Q̇ (14) 

and the specific enthalpy on the outflow boundary is 

hout = Ḣ

out/ṁ (15) 

Now there is a possibility that the refrigerant goes from 

saturated liquid / vapor mix on the inlet boundary to single 

phase flow somewhere within the segment. This can happen 

for example, in the condenser when the refrigerant enters the 

subcooled liquid region. The following is for that specific case, 

but similar equations can be used when the evaporator

refrigerant goes from the saturated vapor / liquid mix region to 

the superheated vapor region.

To check the presence of crossing such a phase boundary, it 

needs to be evaluated whether hout < hsat,l(pout), that is, the 

exit enthalpy is smaller than the saturated liquid enthalpy at the 

exit pressure. If the answer is no, the previous equations 

stand. If the answer is yes, the refrigerant enters the subcooled 

region somewhere within the segment. Once again, the 

distance of the location at which the phase change is

complete, y, is determined. The heat transfer needed to 

condense all vapor is

Q̇

1 = (hin − hsat,l) ∙ ṁ (16)

Then y can be calculated from the following equation

Q̇

1 = y

L ∙ A ∙ α ∙ (Tw − Tin) (17) 
8 

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Next, the E-NTU method, Eq. (7), can be used for the last 

(L − y) long part of the segment to determine the segment out 

temperature Tout by substituting (L − y) ∙ w for the heat transfer 

area and Tsat,l(pout) for Tin. Then Eq. (8) can be used again 

with substituting Tsat,l(pout) for Tin to determine Q̇

2, which is 

now the heat transfer to the wall in the subcooled liquid part of 

the segment. The total heat transfer is the sum of Q̇

1 and Q̇2, 

and Eqs. (14) and (15) can be used again to determine the exit 

specific enthalpy. 

Finally, from the already calculated exit pressure, pout, and the 

specific enthalpy on the exit, hout, all refrigerant material 

properties can be found using the property tables based on p

and h. 

It is also theoretically possible that within one segment the flow 

goes from superheated vapor to subcooled liquid in the 

condenser when the compressor is cycled off and mass flow 

rate quickly drops to near zero. Such case is also treated in the

model with similar methodology, which involves splitting the 

segment into three pieces. The details of this process are not 

given here. 

This completes the explanation of how the outlet boundary flow 

variables of a pipe segment are calculated from the inlet 

boundary flow parameters and wall temperature of that 

segment, for all possible phase change cases. The obtained 

outlet boundary flow variables now can serve as the inlet 

boundary flow variables for the next segment. This method is 

applied to all segments in the pipe, one after another, so the 

pipe flow is solved in what can be called a “marching” scheme 

from the upstream boundary to the downstream boundary of 

the pipe. At the end of this process, a pressure on the outlet 

boundary of the last pipe segment is obtained. This pressure 

can be compared to the pressure in the 0-D volume connected 

to the pipe on the downstream boundary of the pipe. Ideally 

they match within a small error, which would mean the 

refrigerant mass flow rate used in the calculations is 

acceptable as that for the steady state conditions. However, in 

general, the two will differ significantly. One approach could be 

to iterate on the refrigerant mass flow rate until the two 

pressures do match. This was tried, but it actually turned out to 

be very time consuming, as the marching flow calculations 

have to be repeated many times over. The time penalty was so 

high that the Quasi-Transient model showed no improvement 

in speed relative to the Fully-Detailed model. 

Therefore, a different approach was used, in which the 

marching had to be completed only once per pipe per time 

step. Instead of determining the steady state flow following 

from the upstream and downstream 0-D volume conditions in 

each time step, the pipe flow solution is just moved closer to 

this steady state solution in each time step. In each time step, 

the refrigerant pressure at the exit from the line – calculated 

with just one execution of the marching scheme – is compared 

to the pressure in the 0-D volume attached downstream. 

Based on the result of the comparison, a rate of change of the 

refrigerant mass flow rate in the pipe is calculated that allows 

the next time step to have a better match between these

pressures. Because the refrigerant mass flow rate is calculated 

by integrating this rate of change, the refrigerant mass flow 

rate is now a simulation state variable and therefore available 

at the beginning of each time step. A graphical explanation is 

shown in Figure 4. The actual equation applied to calculate the 

derivative of the mass flow rate is 

dṁ

dt = C ∙

pd,calc − pd

pu − pd

∙ ṁ , (18) 

where ṁ is the refrigerant mass flow rate, pu and pd are the 

pressures in the upstream and downstream connected 0-D 

volume blocks, respectively, pd,calc is the 1-D pipe downstream 

boundary pressure calculated in the current time step with one 

sweep of marching, and C is an input parameter that 

determines the strength of the pull towards the steady state 

solution. 

Figure 4. Refrigerant mass flow rate adjustment in Quasi-Transient 1-D 

pipe simulation block (Eq. (18))

Depending on the value of the factor C, the result is a stronger 

or weaker pull of the mass flow rate and all other flow variables

toward the steady state solution prescribed by the attached 0-

D volumes. Proper setting of the input parameter C is 

determined after comparing the results of the Quasi-Transient

model to the results of the Fully-Detailed model.

Treatment of Mass Conservation

Note that the “real” refrigerant mass in the 0-D volumes and 

1-D pipes is an output, and there is nothing implemented in the 

model with the explained methodology that preserves this 

mass over time. In a real system, of course, refrigerant mass is 

preserved, apart from some leakage that usually plays out over 

a very long time. The system does behave somewhat 

differently with different amounts of refrigerant charge. 

Therefore, a fluctuating total refrigerant mass in the system 

gives little hope to match the behavior of a real system. 

The way this issue was addressed in the model was by the 

addition/removal of “artificial” refrigerant mass based on the 

instantaneous total ‘real’ refrigerant mass compared to a target 

or “charge” refrigerant mass. This can be done because in 

each 0-D volume and 1-D pipe at each time step, the ‘real’ 

refrigerant mass is calculated from the volume, the pressure 

and the specific enthalpy, and these masses are summed up 

to provide a simulated refrigerant total mass. A refrigerant 

removal rate linear with the error between this simulated 
9 

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refrigerant total mass and the target refrigerant mass in each 

time step can then be applied. Negative error in this context 

means a need for refrigerant addition. Although somewhat 

arbitrary, it was chosen that mass is added/removed at a single 

point in the system, through the receiver/drier. With this 

implemented, depending on the magnitude of the mass

removal rate coefficient, the calculated refrigerant mass could 

be kept within about 10% of the target.

The Mapped-Component Model

Compared to the Quasi-Transient model, the MappedComponent model represents another step towards increased 

model execution speed at an additional cost of reduced 

accuracy. The Mapped-Component model is created from the 

Quasi-Transient model by replacing the condenser and the 

evaporator sub-models with simplified sub-models that use 

lookup tables. Otherwise, the two models are identical. The 

lookup tables were generated with standalone models of the 

condenser and the evaporator taken out of the Quasi-Transient

model. 

For the condenser, the refrigerant mass flow rate, the air-torefrigerant heat exchange rate, and the refrigerant mass in the 

condenser are each obtained from a separate five-dimensional 

lookup table based on upstream refrigerant pressure, upstream 

refrigerant specific enthalpy, refrigerant pressure drop, air 

mass flow rate, and air inlet temperature. For the evaporator, 

the lookup tables also have to incorporate the relative humidity 

of the incoming air for acceptable accuracy. Therefore, if the 

evaporator had been treated similarly to the condenser, the 

lookup tables would be six-dimensional. Adding a sixth 

dimension to the lookup tables greatly increases the time 

needed to generate them. The hysteresis due to the 

evaporator wall thermal mass is also important when the 

compressor starts cycling for evaporator freeze prevention. To 

solve these issues, the lookup tables for the evaporator were 

split into refrigerant-side and air-side tables coupled through 

the wall temperature. Furthermore, instead of heat exchange 

rate, effectiveness was looked up on the refrigerant side. Using 

the effectiveness proved to be more robust to prevent false 

results in case the conditions were outside the domain of the 

mapping. For the four-dimensional refrigerant-side tables, the 

refrigerant mass flow rate, the refrigerant mass in the 

evaporator, and the wall-to-refrigerant heat transfer 

effectiveness are looked up from the upstream refrigerant 

pressure, upstream refrigerant quality, the refrigerant pressure 

drop, and the temperature differential between the inlet 

refrigerant flow and the wall. For the air side, the air-to-wall 

heat transfer rate is looked up from the air mass flow rate, airin temperature, air-in relative humidity, and the wall 

temperature. Creating these four 4-dimensional maps is much 

more time efficient than creating three maps each with six

dimensions. With this splitting approach, the time needed to 

create the evaporator maps was reduced from 86 to 4 hours. 

Figure 5 shows the input/output variables for the condenser 

performance lookup tables, and Figure 6 shows the input/

output variables for the evaporator performance lookup tables.

Figure 5. Condenser performance lookup tables

Figure 6. Evaporator performance lookup tables

The lookup tables were generated with standalone models of 

the condenser and the evaporator taken out from the QuasiTransient model. For each point in the lookup tables, the 

condenser and evaporator models were run until steady state 

conditions were reached. The heat transfer rates, the

refrigerant mass flow rates, and the refrigerant total masses

were recorded and placed into large arrays that the Simulink 

lookup table blocks of the Mapped-Component model could 

read. (The refrigerant-side evaporator heat transfer rates first 

were processed into effectiveness numbers). This entire 

process was automated. The necessary maps can be created 

with the automated process on an Intel® i7-3520 M 2.9GHz

CPU 64-bit personal computer with 4 GB of RAM in a matter of 

10 to 12 hours.

The lookup tables are used in the following way: refrigerantout enthalpy flow rate is the sum of the refrigerant-in enthalpy 

flow rate and the heat transfer rate to refrigerant, both for the 

condenser and the evaporator. The heat transfer rate in the 

evaporator on the refrigerant side is calculated from the 

effectiveness. Air-out temperature on the evaporator is 

calculated the same way as a segment air-out temperature is 

calculated in the Fully-Detailed model, accounting for 

condensation of water on the metal surfaces, if present. 

Because there are no segments, the iteration on air-out 

temperature has to be carried out only once. Also, there is no 

need for mixing the segment-out air flows. The refrigerant 

mass in the evaporator and in the condenser obtained from the 

lookup tables are added to the refrigerant masses in the rest of 

the system to obtain the total system refrigerant mass. Then, a 

similar adjustment of the refrigerant total mass is applied as in 

the Quasi-Transient model. The refrigerant mass adjustment is 

important; without it, a good match between the data simulated 
10

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with the Mapped-Component model and the steady state 

measured data shown in the next section was not successfully 

achieved.

In the evaporator sub-model, where the wall temperature is a 

simulation model state variable, the equation for the wall 

temperature is the same as in the Fully-Detailed model for a 

segment wall temperature, Eq. (1). Note that here the Q̇

aw and 

Q̇

wr terms are coming from the lookup tables, and there is no 

spatial distribution of wall temperature. One temperature 

describes the wall and Eq. (1) is only used once. This also

means there is no conductive heat transfer in the walls of the 

evaporator in the flow direction as the entire wall is at the same 

temperature.

The assumption of constant wall temperature in space may 

bring in the most significant error. It is a relatively good

assumption in the saturated liquid-vapor mix regions of the 

evaporator, but it represents more deviation from reality in the 

single-phase superheat region where the refrigerant 

temperature is rapidly rising, and the wall temperature is also 

rising as a result.

Results

Verification with Data

Calibration and verification of the three models was completed 

using 22 steady state test bench points from a light-duty 

vehicle A/C system provided by Halla Visteon. These data 

covered a wide range of operating conditions. Because the 

heat exchanger air inflow parameters were known and they 

were constant in time, the cabin model was essentially 

deactivated by setting very large thermal masses.

The data set used for verification included pressures and 

temperatures along the entire refrigerant circuit, properties of 

the upstream and downstream air streams on the heat 

exchangers, and the compressor speed and mass flow rate 

data. More details on the data and its implementation for the 

calibration and verification study can be found in [10]. 

All 22 measurement points in the data set were simulated with 

all three models, and some calibration was done on the heat 

transfer correlation coefficients for the Fully-Detailed model 

only. The Quasi-Transient and Mapped-Component models 

both used the same heat transfer and pressure drop 

correlation coefficients as the Fully-Detailed model. 

In Figures 7a and 7b, the thermodynamic cycles for 

measurement points 4 and 6, respectively, are shown on the 

pressure-enthalpy space for all three models and for the 

measurement. These two points are representative of the 

general quality of the match and represent two points with 

significantly different boundary conditions. Good match 

between the simulation and the measurement can be seen.

Figure 7a Thermodynamic cycle for Test Point 4 in the p-h space

Figure 7b. Thermodynamic cycle for Test Point 6 in the p-h space

Component Level Verification

The refrigerant flow rate, the heat transfer rate on the 

condenser, the heat transfer rate on the evaporator, and the 

evaporator-out air temperature were also generated from the 

full cycle results. The measured and simulated data for these

four variables for all three model versions are included in 

Figures 8a, 8b, 8c, and 8d, respectively.

Figure 8a. Predicted and measured compressor mass flow rate

200 250 300 350 400 450 500

103

Pressure [kPa]

Specific Enthalpy [kJ/kg]

 

mix boundary

measured

Fully-Detailed

Quasi-Transient

Mapped-Component

200 250 300 350 400 450 500

103

Pressure [kPa]

Specific Enthalpy [kJ/kg]

 

mix boundary

measured

Fully-Detailed

Quasi-Transient

Mapped-Component

0 5 10 15 20 0

5

10

15

20

25

30

35

40

45

50

55

Test Point

Mass Flow Rate [g/sec]

Compressor mass flow rate measured

Fully-Detailed

Quasi-Transient

Mapped-Component
11

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 8b. Predicted and measured condenser heat exchange rate

Figure 8c. Predicted and measured evaporator heat exchange rate

Figure 8d. Predicted and measured evaporator air-out temperature

Figures 8a, 8b, 8c, and 8d show that a good match between 

the measured and the simulated data was achieved. As 

expected, the best match is for the Fully-Detailed model, then

the Quasi-Transient, then the Mapped-Component model. The 

average errors for all three models for all four system

variables, that is, for refrigerant mass flow rate, evaporator 

heat exchange rate, condenser heat exchange rate and 

evaporator air-out temperature are shown in Figure 9. All are

expressed in percent except for the evaporator-out air 

temperature for which the error is expressed in degrees

Celsius.

Figure 9. Average prediction errors with the 3 model versions

Comparative Transient Cycle Predictions

Because no measured data for transient processes were 

available, results obtained with the Quasi-Transient and 

Mapped-Component models were compared against results 

obtained with the Fully-Detailed model.

The SC03 cycle was simulated with all three model versions. 

The models were set up for the same exact A/C system, the 

same ambient conditions, and the same cabin initial conditions.

The results of the Quasi-Transient model as compared to the 

Fully-Detailed model for the first 300 seconds of the SC03 

cycle are shown in Figure 10. Similar plots comparing the 

results of the Mapped-Component model to the results of the 

Fully-Detailed model for the first 300 seconds of the SC03 

cycle are shown in Figure 11. 

0 5 10 15 20 0

2

4

6

8

10

12

Test Point

Heat Exchange Rate [kW]

Condenser Performance measured

Fully-Detailed

Quasi-Transient

Mapped-Component

0 5 10 15 20 0

1

2

3

4

5

6

7

8

Test Point

Heat Exchange Rate [kW]

Evaporator Performance measured

Fully-Detailed

Quasi-Transient

Mapped-Component

0 5 10 15 20 0

5

10

15

20

25

Test Point

Temperature [oC]

Evaporator Air-Out Temperature measured

Fully-Detailed

Quasi-Transient

Mapped-Component

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Average Error [% or oC]

mcompr Qevap Qcond Tevap,air,d

. . .

Fully-Detailed

Quasi-Transient

Mapped-Component
12

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Figure 10. Quasi-Transient model predictions vs. Fully-Detailed model 

predictions, first 300 sec of SC03 cycle

The less accurate, but much faster Quasi-Transient model 

results match the results of the Fully-Detailed model well. It is 

notable that the cycling due to evaporator freezing prevention 

starts at around the same time for the Fully-Detailed and the 

Quasi-Transient models. Then, due to slight differences in 

predictions, the start and end points of the cycling periods drift 

away. After some time, the cycling periods may be far off, yet 

such discrepancy does not mean there is a large difference in 

the accuracy of the predictions in general. The discrepancy 

between the Fully-Detailed and the Mapped-Component model 

is much larger; even the timing of the first cycling is 

significantly off.

Figure 11. Mapped-Component model predictions vs. Fully-Detailed

model predictions, first 300 sec of SC03 cycle

0

1

2

3

4

Pressure [bar]

Sytem Minimum Pressure

Fully-Detailed

Quasi-Transient

0

5

10

15

Pressure [bar]

Sytem Maximum Pressure

0

5

10

15

20

Heat Exch.Rate [kW]

Q Evaporator

.

0

10

20

30

Heat Exch.Rate [kW]

Q Condenser

.

0

5

10

Power [kW]

Compressor Power

0 50 100 150 200 250 300

10

20

30

40

Temperature [oC]

Cabin Temperature

time [sec]

0

5

10

15

20

Temperature [oC]

Evaporator Air-out Temperature

0

1

2

3

4

Pressure [bar]

Sytem Minimum Pressure

Fully-Detailed

Mapped-Component

0

5

10

15

20

Pressure [bar]

Sytem Maximum Pressure

0

5

10

15

20

Heat Exch.Rate [kW]

Q Evaporator

.

0

10

20

30

Heat Exch.Rate [kW]

Q Condenser

.

0

5

10

Power [kW]

Compressor Power

0 50 100 150 200 250 300

10

20

30

40

Temperature [oC]

Cabin Temperature

time [sec]

0

5

10

15

20

Temperature [oC]

Evaporator Air-out Temperature
13

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Drive Cycle Averaged Results

For vehicle-focused analysis, agreement of the models over a 

drive cycle is important. Of particular interest are the average 

compressor power and the average heat transfer rates on the 

heat exchangers. These data are shown in Figure 12. Over the 

full SC03 drive cycle, the results with the Quasi-Transient

model were within 1.5% of the results of the Fully-Detailed

model for evaporator and condenser heat transfer and 

compressor power. The Mapped-Component model did not 

match as well. Although the evaporator and condenser heat 

transfer rates were within 1.1% and 4.0% of the Fully-Detailed 

models’, respectively, the compressor power was 18% higher 

than for the Fully-Detailed model. The main reason for this 

larger difference was an underprediction of the evaporator heat 

transfer rate by the Mapped-Component model, which resulted 

in a higher duty-cycle of the compressor.

Figure 12. Comparison of drive cycle averaged performance 

predictions by the three model versions

The drive cycle averaged results also provide an opportunity to 

evaluate the conservativeness of the models. It was shown 

previously [10] that the Fully-Detailed model conserves mass 

extremely well, within 0.001% error or less. The QuasiTransient and the Mapped-Component models both have a 

fluctuating refrigerant mass. The fluctuation is mitigated by the 

addition/removal of some “artificial” mass as explained earlier. 

It is of interest how close these models keep the actual 

refrigerant mass to the target refrigerant mass. For the 

simulation runs shown in Figures 10 and 11, the refrigerant 

mass root mean square errors were 6.18% and 9.31% for the 

Quasi-Transient and the Mapped-Component models, 

respectively. 

Similar analysis can be done for the conservation of energy. 

The compressor power that applies to this discussion is the 

power that actually goes into raising the enthalpy of the 

refrigerant, that is

Pcompr = (hcompr,in − hcompr,out) ∙ qm,compr (19)

(Note the compressor powers in Figures 10,11 and 12

incorporate the compressor mechanical efficiency). In steady

state conditions, the 1st law of thermodynamics applied for the 

system states

Q̇

cond,out − Q̇evap,in = Pcompr (20)

if all heat transfer is assumed to take place in the heat 

exchangers. For transient processes, the terms in Eq. (20) 

have to be integrated over a time period, and the change in 

energy stored in the refrigerant also has to be incorporated to 

be exact. For long periods of simulation, however, the change 

in energy stored in the refrigerant becomes negligible. 

Therefore, the energy conservation of the models will be 

sufficient if the approximation 

� Q̇

cond,out

t2

t1

dt − � Q̇

evap,indt

t2

t1

≅ � Pcompr

t2

t1

dt (21)

holds with good accuracy. The error between the two sides of 

Eq. (21) for the Fully-Detailed model is 1.04%, essentially all of 

which comes from the neglected change in energy stored in 

the refrigerant. The errors in Eq. (21) for the Quasi-Transient

and the Mapped-Component models were also evaluated, and 

were found to be 3.37% for the Quasi-Transient model which is 

reasonable. For the Mapped-Component model, the error was 

1.1%, which is very good but is most likely a result of the 

cancellation of multiple inaccuracies.

Model Execution Speed

These small losses of accuracy come at a large benefit to 

simulation execution speed. In Figure 13, the simulation 

execution speed is compared for the three model versions. The 

speeds were evaluated with the same simulation runs of the 

SC03 cycle that were shown in Figures 10 and 11. The 

simulation execution speed for the Fully-Detailed, QuasiTransient, and Mapped-Component models were 0.10, 0.98,

and 9.96 times faster than real time respectively. For 

reference, “10 times faster than real time” speed means that 

one second of simulated time takes 0.1 second to simulate. 

Figure 13. Comparison of model execution speeds 

Execution speed is also dependent on the number of segments 

in the heat exchanger tubes or plates for the Fully-Detailed and 

the Quasi-Transient models. In both, for the results presented 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Avg.Power or Heat Exhange Rate [kW]

Pcompr,ave Qcond,ave Qevap,ave

. .

Fully-Detailed

Quasi-Transient

Mapped-Component

0

2

4

6

8

10

12

14

0.10 X

0.98 X

9.96 X

Speed [times real time]

Fully-Detailed

Quasi-Transient

Mapped-Component
14

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

here, 18 segments for the condenser flat tubes and 10 

segments for the evaporator plates were used. Fewer 

segments increase simulation speed due to both fewer 

operations per time step and the possibility of using a larger 

time step, but at a cost of reduced accuracy.

Conclusions

A new automotive A/C system simulation tool was previously 

developed on the MATLAB/Simulink platform. That model 

consists of a detailed cooling circuit model and a relatively 

simple cabin model. For the key system simulation blocks, a 

finite volume formulation of the governing equations was used 

on the refrigerant side, which provided a very accurate 

preservation of refrigerant mass and a very accurate energy 

balance. In theory, the model can predict the fast transients 

that occur in an automotive A/C system. However, there was a 

need for much faster models better suited for vehicle drivecycle based evaluation of A/C systems.

Therefore, based on the original model, new model versions 

were created with the goal of greatly increasing the simulation 

speed while minimizing loss of accuracy. The new models 

include the Quasi-Transient model and the MappedComponent model. The Quasi-Transient model provides 

essentially the same accuracy for steady state condition 

prediction as the Fully-Detailed model. 

The Mapped-Component model does lose some accuracy in 

steady state conditions but still performs within about 2% 

average error from the results of the Fully-Detailed model and 

within about 2.5% average error from measured data over a 

wide range of operating conditions. 

The simplified models are not expected to be suitable for 

analyzing problems such as refrigerant redistribution or 

refrigerant peak pressure after compressor shutdown or 

startup. 

Cycle-based averaged results for compressor power and heat 

exchange rates for the SC03 cycle obtained with the QuasiTransient model are within 1.5% of the results of the FullyDetailed model. The Mapped-Component model results are 

within 4.0% of the results of the Fully-Detailed model except for 

the compressor power, which was 18% off. 

The respective speeds at which the simplified Quasi-Transient 

and Mapped-Component models run are 0.98 and 9.96 times

real time speed. This represents a large improvement from the 

Fully-Detailed model, which runs 0.10 times real time speed. 

Conversion from one A/C system model approach to another 

of the three models (Fully-Transient, Quasi-Transient, and 

Mapped-Component) is relatively simple. This allows a new 

model to be developed in a faster version before the results 

are refined using a slower, more detailed solution method as 

needed.

In the trade-off of speed and accuracy, the three models 

occupy very different parts of the scale, and it is believed that 

the simplified models are significant additions to the suite of 

models, especially for vehicle-focused, cycle-based evaluation 

of A/C systems.

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15

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Contact Information

Tibor Kiss (tibor.kiss@nrel.gov)

Jason Lustbader (jason.lustbader@nrel.gov)

Acknowledgments

The authors would like to thank John Rugh and Lawrence 

Chaney of NREL, and John Meyer of Halla Visteon Climate 

Control for their contribution to this project.

The authors would also like to thank David Anderson and Lee 

Slezak, Technology Managers for the U.S. Department of 

Energy’s Advanced Vehicle Technology Analysis and 

Evaluation for sponsoring this work.

Definitions/Abbreviations

0-D zero-dimensional

1-D one-dimensional

A/C air conditioning

E-NTU EffectivenessNumber of Transfer 

Units method

Nomenclature

A Area for heat transfer

α Local heat transfer coefficient

B Bulk modulus

C Pipe flow convergence coefficient

Cp Constant pressure specific heat

DH Hydraulic diameter

f Pipe friction factor

H Enthalpy

Ḣ Enthalpy flow rate

h Specific enthalpy

L Length of pipe or pipe segment

m mass

ṁ Refrigerant mass flow rate

P Power

p Pressure

Q̇ Heat transfer rate

ṁ Refrigerant mass flow rate

ρ Density

ρref Reference or “zero-pressure” density

T Temperature

t Time

U Internal energy

V Volume

v Flow velocity

w Flow channel perimeter

x Coordinate in direction of flow

y Segment length portion

Subscripts:

a Artificial

air Air flow related

ave Time averaged

aw Air to wall

compr Compressor

cond Condenser

d Downstream

evap Evaporator

in On inflow boundary

l Liquid

out On outflow boundary

sat Saturation property

u Upstream

v Vapor

w Wall

wr Wall to refrigerant